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We present a derivation of the star formation rate per comoving volume of quasar host galaxies, derived from stacking analyses of far-infrared to mm-wave photometry of quasars with redshifts 0 < z < 6 and absolute I-band magnitudes −22 > I AB > −32 We use the science demonstration observations of the first ∼ 16 deg 2 from the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) in which there are 240 quasars from the Sloan Digital Sky Survey (SDSS) and a further 171 from the 2dF-SDSS LRG and QSO (2SLAQ) survey. We supplement this data with a compilation of data from IRAS, ISO, Spitzer, SCUBA and MAMBO. H-ATLAS alone statistically detects the quasars in its survey area at > 5σ at 250, 350 and 500 μm. From the compilation as a whole we find striking evidence of downsizing in quasar host galaxy formation: low-luminosity quasars with absolute magnitudes in the range −22 > I AB > −24 have a comoving star formation rate (derived from 100 μm rest-frame luminosities) peaking between redshifts of 1 and 2, while high-luminosity quasars with I AB < −26 have a maximum contribution to the star formation density at z ∼ 3. The volume-averaged star formation rate of −22 > I AB > −24 quasars evolves as (1 + z) 2.3±0.7 at z < 2, but the evolution at higher luminosities is much faster reaching (1 + z) 10±1 at −26 > I AB > −28. We tentatively interpret this as a combination of a declining major merger rate with time and gas consumption reducing fuel for both black hole accretion and star formation.

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